import numpy as np
import pandas as pd
from itertools import cycle
from scipy import interp

# sklearn
from sklearn import metrics
from sklearn.model_selection import train_test_split, StratifiedShuffleSplit
from sklearn import datasets
from sklearn.preprocessing import StandardScaler
from sklearn import preprocessing

# TensorFlow
import tensorflow as tf

# Timer
from timeit import default_timer as timer

# Visualisation libraries

## Text
from colorama import Fore, Back, Style
from IPython.display import Image, display, Markdown, Latex, clear_output

## progressbar
import progressbar

## plotly
from plotly.offline import init_notebook_mode, iplot 
import plotly.graph_objs as go
import plotly.offline as py
from plotly.subplots import make_subplots
import plotly.express as px

## seaborn
import seaborn as sns

## matplotlib
import matplotlib.pyplot as plt
from matplotlib.patches import Ellipse, Polygon
from matplotlib.font_manager import FontProperties
import matplotlib.colors as mcolors
from matplotlib import cm
plt.style.use('seaborn-whitegrid')
plt.rcParams['axes.labelsize'] = 14
plt.rcParams['xtick.labelsize'] = 12
plt.rcParams['ytick.labelsize'] = 12
plt.rcParams['text.color'] = 'k'
%matplotlib inline

import warnings
warnings.filterwarnings("ignore")

Home / Deep Learning

Tensorflow Classifiers

• Tensorflow Linear Classifier
• Tensorflow DNN Classifier
• Tensorflow Boosted Trees Classifier
• Tensorflow Boosted Trees Classifier with Feature Importance Analysis

In this article, we demonstrate implementing the Tensorflow Linear classifier model by an example. The details regarding this dataset can be found in the Diagnostic Wisconsin Breast Cancer Database.

data = datasets.load_breast_cancer()
Data = pd.DataFrame(data['data'], columns = [x.title() for x in data['feature_names']])
Labels_dict = dict(zip(list(np.sort(np.unique(data['target'].tolist()))),
                       list([x.title() for x in data['target_names']])))
Target = 'Diagnosis'
Data[Target] = data['target']
display(Data)
print(data['DESCR'])

	Mean Radius	Mean Texture	Mean Perimeter	Mean Area	Mean Smoothness	Mean Compactness	Mean Concavity	Mean Concave Points	Mean Symmetry	Mean Fractal Dimension	...	Worst Texture	Worst Perimeter	Worst Area	Worst Smoothness	Worst Compactness	Worst Concavity	Worst Concave Points	Worst Symmetry	Worst Fractal Dimension	Diagnosis
0	17.99	10.38	122.80	1001.0	0.11840	0.27760	0.30010	0.14710	0.2419	0.07871	...	17.33	184.60	2019.0	0.16220	0.66560	0.7119	0.2654	0.4601	0.11890	0
1	20.57	17.77	132.90	1326.0	0.08474	0.07864	0.08690	0.07017	0.1812	0.05667	...	23.41	158.80	1956.0	0.12380	0.18660	0.2416	0.1860	0.2750	0.08902	0
2	19.69	21.25	130.00	1203.0	0.10960	0.15990	0.19740	0.12790	0.2069	0.05999	...	25.53	152.50	1709.0	0.14440	0.42450	0.4504	0.2430	0.3613	0.08758	0
3	11.42	20.38	77.58	386.1	0.14250	0.28390	0.24140	0.10520	0.2597	0.09744	...	26.50	98.87	567.7	0.20980	0.86630	0.6869	0.2575	0.6638	0.17300	0
4	20.29	14.34	135.10	1297.0	0.10030	0.13280	0.19800	0.10430	0.1809	0.05883	...	16.67	152.20	1575.0	0.13740	0.20500	0.4000	0.1625	0.2364	0.07678	0
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
564	21.56	22.39	142.00	1479.0	0.11100	0.11590	0.24390	0.13890	0.1726	0.05623	...	26.40	166.10	2027.0	0.14100	0.21130	0.4107	0.2216	0.2060	0.07115	0
565	20.13	28.25	131.20	1261.0	0.09780	0.10340	0.14400	0.09791	0.1752	0.05533	...	38.25	155.00	1731.0	0.11660	0.19220	0.3215	0.1628	0.2572	0.06637	0
566	16.60	28.08	108.30	858.1	0.08455	0.10230	0.09251	0.05302	0.1590	0.05648	...	34.12	126.70	1124.0	0.11390	0.30940	0.3403	0.1418	0.2218	0.07820	0
567	20.60	29.33	140.10	1265.0	0.11780	0.27700	0.35140	0.15200	0.2397	0.07016	...	39.42	184.60	1821.0	0.16500	0.86810	0.9387	0.2650	0.4087	0.12400	0
568	7.76	24.54	47.92	181.0	0.05263	0.04362	0.00000	0.00000	0.1587	0.05884	...	30.37	59.16	268.6	0.08996	0.06444	0.0000	0.0000	0.2871	0.07039	1

569 rows × 31 columns

.. _breast_cancer_dataset:

Breast cancer wisconsin (diagnostic) dataset
--------------------------------------------

**Data Set Characteristics:**

    :Number of Instances: 569

    :Number of Attributes: 30 numeric, predictive attributes and the class

    :Attribute Information:
        - radius (mean of distances from center to points on the perimeter)
        - texture (standard deviation of gray-scale values)
        - perimeter
        - area
        - smoothness (local variation in radius lengths)
        - compactness (perimeter^2 / area - 1.0)
        - concavity (severity of concave portions of the contour)
        - concave points (number of concave portions of the contour)
        - symmetry
        - fractal dimension ("coastline approximation" - 1)

        The mean, standard error, and "worst" or largest (mean of the three
        worst/largest values) of these features were computed for each image,
        resulting in 30 features.  For instance, field 0 is Mean Radius, field
        10 is Radius SE, field 20 is Worst Radius.

        - class:
                - WDBC-Malignant
                - WDBC-Benign

    :Summary Statistics:

    ===================================== ====== ======
                                           Min    Max
    ===================================== ====== ======
    radius (mean):                        6.981  28.11
    texture (mean):                       9.71   39.28
    perimeter (mean):                     43.79  188.5
    area (mean):                          143.5  2501.0
    smoothness (mean):                    0.053  0.163
    compactness (mean):                   0.019  0.345
    concavity (mean):                     0.0    0.427
    concave points (mean):                0.0    0.201
    symmetry (mean):                      0.106  0.304
    fractal dimension (mean):             0.05   0.097
    radius (standard error):              0.112  2.873
    texture (standard error):             0.36   4.885
    perimeter (standard error):           0.757  21.98
    area (standard error):                6.802  542.2
    smoothness (standard error):          0.002  0.031
    compactness (standard error):         0.002  0.135
    concavity (standard error):           0.0    0.396
    concave points (standard error):      0.0    0.053
    symmetry (standard error):            0.008  0.079
    fractal dimension (standard error):   0.001  0.03
    radius (worst):                       7.93   36.04
    texture (worst):                      12.02  49.54
    perimeter (worst):                    50.41  251.2
    area (worst):                         185.2  4254.0
    smoothness (worst):                   0.071  0.223
    compactness (worst):                  0.027  1.058
    concavity (worst):                    0.0    1.252
    concave points (worst):               0.0    0.291
    symmetry (worst):                     0.156  0.664
    fractal dimension (worst):            0.055  0.208
    ===================================== ====== ======

    :Missing Attribute Values: None

    :Class Distribution: 212 - Malignant, 357 - Benign

    :Creator:  Dr. William H. Wolberg, W. Nick Street, Olvi L. Mangasarian

    :Donor: Nick Street

    :Date: November, 1995

This is a copy of UCI ML Breast Cancer Wisconsin (Diagnostic) datasets.
https://goo.gl/U2Uwz2

Features are computed from a digitized image of a fine needle
aspirate (FNA) of a breast mass.  They describe
characteristics of the cell nuclei present in the image.

Separating plane described above was obtained using
Multisurface Method-Tree (MSM-T) [K. P. Bennett, "Decision Tree
Construction Via Linear Programming." Proceedings of the 4th
Midwest Artificial Intelligence and Cognitive Science Society,
pp. 97-101, 1992], a classification method which uses linear
programming to construct a decision tree.  Relevant features
were selected using an exhaustive search in the space of 1-4
features and 1-3 separating planes.

The actual linear program used to obtain the separating plane
in the 3-dimensional space is that described in:
[K. P. Bennett and O. L. Mangasarian: "Robust Linear
Programming Discrimination of Two Linearly Inseparable Sets",
Optimization Methods and Software 1, 1992, 23-34].

This database is also available through the UW CS ftp server:

ftp ftp.cs.wisc.edu
cd math-prog/cpo-dataset/machine-learn/WDBC/

.. topic:: References

   - W.N. Street, W.H. Wolberg and O.L. Mangasarian. Nuclear feature extraction 
     for breast tumor diagnosis. IS&T/SPIE 1993 International Symposium on 
     Electronic Imaging: Science and Technology, volume 1905, pages 861-870,
     San Jose, CA, 1993.
   - O.L. Mangasarian, W.N. Street and W.H. Wolberg. Breast cancer diagnosis and 
     prognosis via linear programming. Operations Research, 43(4), pages 570-577, 
     July-August 1995.
   - W.H. Wolberg, W.N. Street, and O.L. Mangasarian. Machine learning techniques
     to diagnose breast cancer from fine-needle aspirates. Cancer Letters 77 (1994) 
     163-171.

Features with high variance

Moreover, high variance for some features can hurt our modeling process. For this reason, we would like to standardize features by removing the mean and scaling to unit variance.

def Feature_Normalize(X, PD):
    def List_Break(mylist, n = PD['word_break']):
        Out = []
        for x in mylist:
            y = x.split()
            if len(y)> n:
                z = ' '.join(y[:n])
                sep = np.arange(0, len(y), n)[1:]
                for n in sep:
                    z = z + '\n'+ ' '.join(y[n:])
            else:
                z = ' '.join(y)
            Out.append(z)
        return Out

    X = Data.drop(columns = [Target])
    y = Data[Target]

    scaler = preprocessing.StandardScaler()
    X_std = scaler.fit_transform(X)
    X_std = pd.DataFrame(data = X_std, columns = X.columns)

    fig, ax = plt.subplots(2, 1, figsize = PD['figsize'])
    ax = ax.ravel()
    CP = [sns.color_palette("OrRd", 20), sns.color_palette("Greens", X.shape[1])]
    Names = ['Variance of the Features', 'Variance of the Features (Standardized)']
    Sets = [X, X_std]
    kws = dict(label='Feature\nVariance', aspect=10, shrink= .3)
    for i in range(len(ax)):
        Temp = Sets[i].var().sort_values(ascending = False).to_frame(name= 'Variance').round(2).T
        _ = sns.heatmap(Temp, ax=ax[i], annot=True, square=True,  cmap = CP[i],
                        linewidths = 0.8, vmin=0, vmax=Temp.max(axis =1)[0],  annot_kws={"size": PD['annot_text_size']},
                        cbar_kws=kws)
        if not PD['word_break'] == None:
            mylist = List_Break(Temp.T.index.tolist())
            _ = ax[i].xaxis.set_ticklabels(mylist)
        _ = ax[i].set_yticklabels('')
        _ = ax[i].set_title(Names[i], weight='bold', fontsize = 14)
        _ = ax[i].set_aspect(1)
        del Temp
    plt.subplots_adjust(hspace=PD['hspace'])
    Out = pd.DataFrame(data = X_std, columns = X.columns.tolist())
    return Out

X = Data.drop(columns = [Target])
y = Data[Target]

PD = dict(figsize = (20, 8), hspace = 0.2, annot_text_size = 12, word_break = None)
X = Feature_Normalize(X, PD)

Train and Test sets

def DatasetTargetDist(Inp, Target, Labels_dict, PD):
    # Table
    Table = Inp[Target].value_counts().to_frame('Count').reset_index(drop = False).rename(columns = {'index':Target})
    Table[Target] = Table[Target].replace(Labels_dict)
    Table['Percentage'] = np.round(100*(Table['Count']/Table['Count'].sum()),2)
    fig = make_subplots(rows=1, cols=2, horizontal_spacing = 0.02, column_widths=PD['column_widths'],
                        specs=[[{"type": "table"},{"type": "pie"}]])

    # Right
    fig.add_trace(go.Pie(labels=Table[Target].values, values=Table['Count'].values,
                         pull=PD['pull'], textfont=dict(size= PD['textfont']),
                         marker=dict(colors = PD['PieColors'], line=dict(color='black', width=1))), row=1, col=2)
    fig.update_traces(hole=PD['hole'])
    fig.update_layout(height = PD['height'], legend=dict(orientation="v"), legend_title_text= PD['legend_title'])
    
    # Left
    T = Table.copy()
    T['Percentage'] = T['Percentage'].map(lambda x: '%%%.2f' % x)
    Temp = []
    for i in T.columns:
        Temp.append(T.loc[:,i].values)

    fig.add_trace(go.Table(header=dict(values = list(Table.columns), line_color='darkslategray',
                                       fill_color= PD['TableColors'][0], align=['center','center'],
                                       font=dict(color='white', size=12), height=25), columnwidth = PD['tablecolumnwidth'],
                           cells=dict(values=Temp, line_color='darkslategray',
                                      fill=dict(color= [PD['TableColors'][1], PD['TableColors'][1]]),
                                  align=['center', 'center'], font_size=12, height=20)), 1, 1)

    fig.update_layout(title={'text': '<b>' + Target + '<b>', 'x':PD['title_x'],
                                     'y':PD['title_y'], 'xanchor': 'center', 'yanchor': 'top'})
    fig.show()

Pull = [0 for x in range((len(Labels_dict)-1))]
Pull.append(.05)
PD = dict(PieColors = ['SeaGreen','FireBrick'],
          TableColors = ['Navy','White'], hole = .4,
          column_widths=[0.6, 0.4],textfont = 14, height = 350, tablecolumnwidth = [0.20, 0.12, 0.15],
          pull = Pull, legend_title = Target, title_x = 0.5, title_y = 0.8)
del Pull
DatasetTargetDist(Data, Target, Labels_dict, PD)

StratifiedKFold is a variation of k-fold which returns stratified folds: each set contains approximately the same percentage of samples of each target class as the complete set.

Test_Size = 0.3
sss = StratifiedShuffleSplit(n_splits=1, test_size=Test_Size, random_state=42)
_ = sss.get_n_splits(X, y)
# For Tensorflow
X.columns = [x.replace(' ','_') for x in X.columns]

for train_index, test_index in sss.split(X, y):
    # X
    if isinstance(X, pd.DataFrame):
        X_train, X_test = X.loc[train_index], X.loc[test_index]
    else:
        X_train, X_test = X[train_index], X[test_index]
    # y    
    if isinstance(y, pd.Series):
        y_train, y_test = y[train_index], y[test_index]
    else:
        y_train, y_test = y[train_index], y[test_index]
del sss

def Train_Test_Dist(X_train, y_train, X_test, y_test, PD, Labels_dict = Labels_dict):
    def ToSeries(x):
        if not isinstance(x, pd.Series):
            Out = pd.Series(x)
        else:
            Out = x.copy()
        return Out
    
    fig = make_subplots(rows=1, cols=3, horizontal_spacing = 0.02, column_widths= PD['column_widths'],
                        specs=[[{"type": "table"},{'type':'domain'}, {'type':'domain'}]])
    # Right
    C = 2
    for y in [ToSeries(y_train).replace(Labels_dict), ToSeries(y_test).replace(Labels_dict)]:
        fig.add_trace(go.Pie(labels= list(Labels_dict.values()),
                             values= y.value_counts().values, pull=PD['pull'],
                             textfont=dict(size=PD['textfont']),
                             marker=dict(colors = PD['PieColors'],
                             line=dict(color='black', width=1))), row=1, col=C)
        fig.update_traces(hole=.5)
        fig.update_layout(legend=dict(orientation="v"), legend_title_text= PD['legend_title'])
        C+=1
    
    # Left
    
    # Table
    Table = pd.DataFrame(data={'Set':['X_train','X_test','y_train','y_test'],
                       'Shape':[X_train.shape, X_test.shape, y_train.shape, y_test.shape]}).astype(str)
    T = Table.copy()
    Temp = []
    for i in T.columns:
        Temp.append(T.loc[:,i].values)
        
    TableColors = PD['TableColors']
    fig.add_trace(go.Table(header=dict(values = list(Table.columns), line_color='darkslategray',
                                       fill_color= TableColors[0], align=['center','center'],
                                       font=dict(color='white', size=12), height=25), columnwidth = PD['tablecolumnwidth'],
                           cells=dict(values=Temp, line_color='darkslategray',
                                      fill=dict(color= [TableColors[1], TableColors[1]]),
                                  align=['center', 'center'], font_size=12, height=20)), 1, 1)
    fig.update_layout(title={'text': '<b>' + 'Dataset Distribution' + '<b>', 'x':PD['title_x'],
                                     'y':PD['title_y'], 'xanchor': 'center', 'yanchor': 'top'})
    if not PD['height'] == None:
        fig.update_layout(height = PD['height'])
    fig.show()
    
PD.update(dict(PieColors = ['FireBrick', 'SeaGreen'], column_widths=[0.3, 0.3, 0.3],
               tablecolumnwidth = [0.2, 0.4], height = 350, legend_title = Target))

Train_Test_Dist(X_train, y_train, X_test, y_test, PD)

Feature Columns

Create the feature columns, using the original numeric columns as is and one-hot-encoding categorical variables.

def Feat_Columns(Inp, Numeric = False, disp_dtype = False):
    '''
    Feature Columns function
    Input: Dataset
    Output: Tensorflow Feature Column List
    '''
    if not Numeric:
        Numeric = ['int64', 'int32', 'float64', 'float32']
    Temp = Inp.dtypes.reset_index(drop = False)
    Temp.columns = ['Features', 'Data Type']
    Temp['Data Type'] = Temp['Data Type'].astype(str)
    # Numeric_Columns
    Numeric_Columns = Temp.loc[Temp['Data Type'].isin(Numeric), 'Features'].tolist()
    # Categorical_Columns
#     Categorical_Columns = Temp.loc[(~Temp['Data Type'].isin(Numeric)), 'Features'].tolist()
    Categorical_Columns = Temp.loc[Temp['Data Type'] == 'object','Features'].tolist()
    if disp_dtype:
        display(pd.DataFrame({'Numeric Columns': [', '.join(Numeric_Columns)],
                  'Categorical Columns': [', '.join(Categorical_Columns)]}, index = ['Columns']).T.style)
    # Feature Columns
    feature_columns = []
    if len(Categorical_Columns)>0:
        for feature_name in Categorical_Columns:
            vocabulary = Inp[feature_name].unique()
            feature_columns.append(tf.feature_column.indicator_column(\
                                      tf.feature_column.categorical_column_with_vocabulary_list(feature_name, vocabulary)))
    if len(Numeric_Columns)>0:
        for feature_name in Numeric_Columns:
            feature_columns.append(tf.feature_column.numeric_column(feature_name))
    return feature_columns

Input Function

The input function specifies how data is converted to a tf.data.Dataset that feeds the input pipeline in a streaming fashion. Moreover, an input function is a function that returns a tf.data.Dataset object which outputs the following two-element tuple:

• features - A Python dictionary in which:
  • Each key is the name of a feature.
  • Each value is an array containing all of that feature's values.
• label - An array containing the values of the label for every example.

def make_input_fn(X, y, inmemory_train = False, n_epochs= None, shuffle=True, batch_size = 256):
    # Not In memory Training
    if not inmemory_train:
        def input_fn():
            dataset = tf.data.Dataset.from_tensor_slices((X.to_dict(orient='list'), y))
            if shuffle:
                dataset = dataset.shuffle(1000)
            dataset = (dataset.repeat(n_epochs).batch(batch_size))
            return dataset
    # In memory Training
    if inmemory_train:
        y = np.expand_dims(y, axis=1)
        def input_fn():
            return dict(X), y
    # End
    return input_fn

Building the input pipeline

my_feature_columns = Feat_Columns(X)
# Training and evaluation input functions.
train_input_fn = make_input_fn(X_train, y_train)
eval_input_fn = make_input_fn(X_test, y_test, shuffle=False, n_epochs=1)

Modeling: Boosted Trees Classifier

# Classifier
tf.keras.backend.clear_session()
IT = int(1e3)
params = {'n_trees': 50, 'max_depth': 3, 'n_batches_per_layer': 1, 'center_bias': True}
classifier =  tf.estimator.BoostedTreesClassifier(my_feature_columns, **params)
# Train model.
start = timer()
classifier.train(train_input_fn, max_steps = IT)
CPU_Time = timer() - start
# Evaluation.
results = classifier.evaluate(eval_input_fn)
clear_output()
results['CPU Time'] = CPU_Time
display(pd.DataFrame(results, index = ['']).round(4))

	accuracy	accuracy_baseline	auc	auc_precision_recall	average_loss	label/mean	loss	precision	prediction/mean	recall	global_step	CPU Time
	0.9532	0.6257	0.9952	0.9972	0.0913	0.6257	0.0913	0.9626	0.6292	0.9626	156	6.5469

ROC Curves

def ROC_Curve(y_test, probs, n_classes, FS = 7, ax = False, pad = 0.01):
    # converting y_test to categorical
    y_test_cat = tf.keras.utils.to_categorical(y_test, num_classes=n_classes, dtype='float32')
    # Compute ROC curve and ROC area for each class
    fpr = dict()
    tpr = dict()
    roc_auc = dict()
    for i in range(n_classes):
        fpr[i], tpr[i], _ = metrics.roc_curve(y_test_cat[:, i], probs[:, i])
        roc_auc[i] = metrics.auc(fpr[i], tpr[i])

    # Compute micro-average ROC curve and ROC area
    fpr["micro"], tpr["micro"], _ = metrics.roc_curve(y_test_cat.ravel(), probs.ravel())
    roc_auc["micro"] = metrics.auc(fpr["micro"], tpr["micro"])

    # First aggregate all false positive rates
    all_fpr = np.unique(np.concatenate([fpr[i] for i in range(n_classes)]))

    # Then interpolate all ROC curves at this points
    mean_tpr = np.zeros_like(all_fpr)
    for i in range(n_classes):
        mean_tpr += interp(all_fpr, fpr[i], tpr[i])

    # Finally average it and compute AUC
    mean_tpr /= n_classes

    fpr["macro"] = all_fpr
    tpr["macro"] = mean_tpr
    roc_auc["macro"] = metrics.auc(fpr["macro"], tpr["macro"])

    fig = go.Figure()
    fig.add_trace(go.Scatter(x=[0, 1], y=[0, 1], name = 'FPR = TPR', line = dict(color='Black', width=2, dash='dash')))
    fig.add_trace(go.Scatter(x=fpr["micro"], y=tpr["micro"], mode='lines', marker_color = 'deeppink',
                             name='micro-average ROC curve (area = {0:0.2f})'.format(roc_auc["micro"])))
    fig.add_trace(go.Scatter(x=fpr["macro"], y=tpr["macro"], mode='lines', marker_color = 'navy',
                             name='macro-average ROC curve (area = {0:0.2f})'.format(roc_auc["macro"])))

    colors = cycle(['Aqua', 'DarkOrange', 'CornflowerBlue'])
    for i, color in zip(range(n_classes), colors):
        _ = fig.add_trace(go.Scatter(x = fpr[i], y = tpr[i], mode='lines', marker_color= px.colors.sequential.Rainbow,
                                     name='ROC curve of class {0} (area = {1:0.2f})'.format(i, roc_auc[i])))

    # Background
    fig.update_layout(plot_bgcolor= 'white')
    fig.update_xaxes(showline=True, linewidth=1, linecolor='Lightgray', mirror=True,
                     zeroline=True, zerolinewidth=1, zerolinecolor='Black',
                     showgrid=True, gridwidth=1, gridcolor='Lightgray', range =[-pad, 1+pad],
                     title = 'False Positive Rate (FPR)')
    fig.update_yaxes(showline=True, linewidth=1, linecolor='Lightgray', mirror=True,
                     zeroline=True, zerolinewidth=1, zerolinecolor='Black',
                     showgrid=True, gridwidth=1, gridcolor='Lightgray', range =[-pad, 1+pad],
                     title = 'True Positive Rate (TPR)')
    fig.update_yaxes(scaleanchor = "x", scaleratio = 1)
    fig.update_layout(height = 600, width = 810)
    fig.update_layout(title={'text': '<b>' + 'Receiver Operating Characteristic (ROC) Curves' + '<b>', 'x': .5,
                                         'y': .9, 'xanchor': 'center', 'yanchor': 'top'})
    fig.show()

pred_dicts = list(classifier.predict(eval_input_fn))
clear_output()
probs = np.array([pred['probabilities'] for pred in pred_dicts])    
ROC_Curve(y_test, probs, n_classes = len(Labels_dict), FS = 8)

Confusion Matrix

The confusion matrix allows for visualization of the performance of an algorithm. Note that due to the size of data, here we don't provide a Cross-validation evaluation. In general, this type of evaluation is preferred.

def Confusion_Mat(CM_Train, CM_Test, PD, n_splits = 10):
    if n_splits == None:
        Titles = ['Train Set', 'Test Set']
    else:
        Titles = ['Train Set (CV = % i)' % n_splits, 'Test Set (CV = % i)' % n_splits]
    CM = [CM_Train, CM_Test]
    Cmap = ['Greens', 'YlGn','Blues', 'PuBu']
    for i in range(2):
        fig, ax = plt.subplots(1, 2, figsize= PD['FS'])
        fig.suptitle(Titles[i], weight = 'bold', fontsize = 16)
        _ = sns.heatmap(CM[i], annot=True, annot_kws={"size": PD['annot_kws']}, cmap=Cmap[2*i], ax = ax[0],
                        linewidths = 0.2, cbar_kws={"shrink": PD['shrink']})
        _ = ax[0].set_title('Confusion Matrix');
        Temp = np.round(CM[i].astype('float') / CM[i].sum(axis=1)[:, np.newaxis], 2)
        _ = sns.heatmap(Temp,
                        annot=True, annot_kws={"size": PD['annot_kws']}, cmap=Cmap[2*i+1], ax = ax[1],
                       linewidths = 0.4, vmin=0, vmax=1, cbar_kws={"shrink": PD['shrink']})
        _ = ax[1].set_title('Normalized Confusion Matrix');

        for a in ax:
            _ = a.set_xlabel('Predicted labels')
            _ = a.set_ylabel('True labels'); 
            _ = a.xaxis.set_ticklabels(PD['Labels'])
            _ = a.yaxis.set_ticklabels(PD['Labels'])
            _ = a.set_aspect(1)

Train in Memory

An alternative way to train a model with boosting performance is using the train_in_memory feature. However, if there is no issue with performance or long training time is not a concern, training without this feature is recommended [2]. Furthermore, our observations have shown that using train_in_memory not always increases the performance of the training.

in_memory_params = dict(params)
in_memory_params['n_batches_per_layer'] = 1
# In-memory input_fn does not use batching.
train_input_fn = make_input_fn(X_train, y_train, inmemory_train = True)

# Classifier
tf.keras.backend.clear_session()
classifier =  tf.estimator.BoostedTreesClassifier(my_feature_columns, train_in_memory=True, **in_memory_params)
# Train model.
start = timer()
classifier.train(train_input_fn, max_steps = IT)
CPU_Time = timer() - start
# Evaluation.
results = classifier.evaluate(eval_input_fn)
clear_output()
results['CPU Time'] = CPU_Time
display(pd.DataFrame(results, index = ['']).round(4))

	accuracy	accuracy_baseline	auc	auc_precision_recall	average_loss	label/mean	loss	precision	prediction/mean	recall	global_step	CPU Time
	0.9649	0.6257	0.9776	0.9847	0.1443	0.6257	0.1443	0.955	0.6403	0.9907	153	9.3362

ROC Curves

pred_dicts = list(classifier.predict(eval_input_fn))
clear_output()
probs = np.array([pred['probabilities'] for pred in pred_dicts])    
ROC_Curve(y_test, probs, n_classes = len(Labels_dict), FS = 8)

Feature Importance

We can investigate the feature importance of an artificial classification task. This is similar to that of scikit-learn and has been outlined in [6].

pred_dicts = list(classifier.experimental_predict_with_explanations(eval_input_fn))
clear_output()

# Create DFC Pandas dataframe.
labels = y_test
probs = pd.Series([pred['probabilities'][1] for pred in pred_dicts])
df_dfc = pd.DataFrame([pred['dfc'] for pred in pred_dicts])
df_dfc.columns = [x.replace('_',' ') for x in df_dfc.columns]
display(df_dfc.describe().T.style.background_gradient(subset= ['mean'], cmap='RdYlGn')\
        .background_gradient(subset= ['std'], cmap='RdYlGn')\
        .background_gradient(subset= ['min'], cmap='hot')\
        .background_gradient(subset= ['max'], cmap='winter')
        .set_precision(4).format({'count': "{:.0f}"}))

	count	mean	std	min	25%	50%	75%	max
Worst Concave Points	171	0.0333	0.0933	-0.2053	-0.0838	0.0932	0.0956	0.2176
Worst Texture	171	0.0128	0.0405	-0.1002	-0.0018	0.0173	0.0216	0.2330
Worst Perimeter	171	-0.0004	0.0651	-0.1504	-0.0804	0.0470	0.0531	0.0975
Concavity Error	171	-0.0105	0.0170	-0.0679	-0.0295	0.0000	0.0000	0.0450
Worst Smoothness	171	-0.0356	0.0490	-0.2036	-0.0921	-0.0033	0.0013	0.0924
Worst Concavity	171	-0.0131	0.0228	-0.0748	-0.0383	-0.0017	0.0031	0.0499
Mean Concave Points	171	0.0065	0.0489	-0.2043	-0.0387	0.0250	0.0279	0.2167
Mean Texture	171	-0.0407	0.0689	-0.2527	-0.1216	-0.0012	0.0080	0.2026
Worst Radius	171	0.0183	0.0669	-0.1410	-0.0646	0.0657	0.0667	0.1056
Worst Area	171	-0.0007	0.0462	-0.1439	-0.0337	0.0264	0.0310	0.0937
Mean Area	171	0.0040	0.0071	-0.0187	-0.0002	0.0079	0.0079	0.0434
Mean Compactness	171	0.0011	0.0086	-0.0466	-0.0007	0.0003	0.0020	0.0448
Mean Perimeter	171	0.0002	0.0040	-0.0211	-0.0001	0.0000	0.0006	0.0227
Worst Compactness	171	0.0107	0.0149	-0.0519	-0.0029	0.0203	0.0227	0.0390
Area Error	171	0.0071	0.0347	-0.1253	-0.0333	0.0259	0.0279	0.1259
Mean Smoothness	171	-0.0004	0.0093	-0.0437	-0.0011	-0.0005	0.0002	0.0538
Worst Symmetry	171	0.0051	0.0103	-0.0070	0.0000	0.0015	0.0034	0.0642
Symmetry Error	171	-0.0001	0.0028	-0.0210	0.0000	0.0000	0.0001	0.0112
Compactness Error	171	0.0014	0.0170	-0.1222	-0.0000	0.0005	0.0014	0.0554
Mean Concavity	171	0.0016	0.0076	-0.0157	-0.0002	0.0002	0.0006	0.0575
Smoothness Error	171	0.0069	0.0126	-0.0432	0.0000	0.0054	0.0071	0.0793
Radius Error	171	0.0002	0.0009	-0.0060	0.0000	0.0000	0.0001	0.0033
Texture Error	171	-0.0001	0.0030	-0.0339	0.0000	0.0000	0.0000	0.0069
Concave Points Error	171	0.0009	0.0053	-0.0033	0.0000	0.0000	0.0000	0.0501
Fractal Dimension Error	171	0.0002	0.0023	-0.0032	0.0000	0.0000	0.0000	0.0303
Mean Fractal Dimension	171	0.0007	0.0054	-0.0106	0.0000	0.0000	0.0000	0.0462
Mean Radius	171	0.0001	0.0025	-0.0191	0.0000	0.0000	0.0000	0.0212
Mean Symmetry	171	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
Perimeter Error	171	0.0043	0.0072	-0.0450	0.0000	0.0052	0.0067	0.0385
Worst Fractal Dimension	171	-0.0014	0.0119	-0.0650	-0.0007	-0.0000	0.0001	0.0635

A nice property of DFCs is that the sum of the contributions + the bias is equal to the prediction for a given example.

# Sum of DFCs + bias == probabality.
bias = pred_dicts[0]['bias']
dfc_prob = df_dfc.sum(axis=1) + bias
np.testing.assert_almost_equal(dfc_prob.values, probs.values)

Feature Importance for a patient

Plot DFCs for an individual patient which is color-coded based on the contributions' directionality and add the feature values on the figure.

def _add_feature_values(feature_values, ax, colors):
    """Display feature's values on left of plot."""
    x_coord = ax.get_xlim()[0]
    OFFSET = 0.15
    for y_coord, (feat_name, feat_val) in enumerate(feature_values.items()):
        t = plt.text(x_coord, y_coord - OFFSET, '{}'.format(feat_val), size=12)
        t.set_bbox(dict(facecolor= colors[y_coord], alpha=0.25))
    font = FontProperties()
#     font.set_weight('bold')
    t = plt.text(x_coord, y_coord + 1 - OFFSET, 'Feature\nValue', fontproperties=font, size=13)

def _xLims(ax):
    Temp = np.linspace(-1,1,21, endpoint=True)
    Temp = np.round(Temp,1)
    xlims = ax.get_xlim()
    for l, r in list(zip(Temp[:-1],Temp[1:])):
        if l<= xlims[0] < r:
            Left = l
        if l<= xlims[1] < r:
            Right = r
    return [Left, Right]

def Plot_Example(example, TOP_N = 10, Pos_Color = 'LimeGreen', Neg_Color = 'OrangeRed', Maps = None, FS = (13, 7)):
    # Sorting by absolute value
    sorted_ix = example.abs().sort_values()[-TOP_N:].index
    example = example[sorted_ix]
    
    fig, ax = plt.subplots(1, 1, figsize= FS)
    Temp = example.to_frame('Value').sort_index(ascending= False)
    Temp0 = Temp.copy(); Temp0[Temp0 < 0] = np.nan
    _ = Temp0.plot(kind='barh', color= Pos_Color, edgecolor = 'white', hatch = '///', legend=None, alpha=0.75, ax = ax)
    Temp0 = Temp.copy(); Temp0[Temp0 >= 0] = np.nan
    _ = Temp0.plot(kind='barh', color= Neg_Color, edgecolor = 'white', hatch = '///', legend=None, alpha=0.75, ax = ax)
    _ = Temp.plot(kind='barh', color='None', edgecolor = 'Black', legend=None, alpha=1, lw=1.2, ax = ax)
    del Temp, Temp0
    _ = ax.grid(False, axis='y')
    # x axis Limits
    _ = ax.set_xlim(_xLims(ax))
    
    # Add feature values.
    Temp = X_test.copy()
    Temp.columns = [x.replace('_',' ') for x in Temp.columns]
    if not Maps == None:
        for c in Maps.keys():
            Temp[c] = Temp[c].map(Maps[c])
  
    colors = example.map(lambda x: Pos_Color if x >= 0 else Neg_Color).tolist()
    _add_feature_values(Temp.iloc[ID][sorted_ix].round(4), ax, colors)
    return ax

ID = 61
Tops = X_train.shape[1]
ax = Plot_Example(df_dfc.iloc[ID], TOP_N = Tops, FS = (13, 16))
_ = ax.set_title('Feature contributions for example patient {} from the Test set\n Pred: {:1.2f}; Label: {}'
                 .format(ID, probs[ID], labels.iloc[ID]))
_ = ax.set_xlabel('Contribution to Predicted Probability', size=14)

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References

1. Detrano, R., Janosi, A., Steinbrunn, W., Pfisterer, M., Schmid, J.J., Sandhu, S., Guppy, K.H., Lee, S. and Froelicher, V., 1989. International application of a new probability algorithm for the diagnosis of coronary artery disease. The American journal of cardiology, 64(5), pp.304-310.

2. Aha, D. and Kibler, D., 1988. Instance-based prediction of heart-disease presence with the Cleveland database. University of California, 3(1), pp.3-2.

3. Gennari, J.H., Langley, P. and Fisher, D., 1989. Models of incremental concept formation. Artificial intelligence, 40(1-3), pp.11-61.

4. Regression analysis Wikipedia page
5. Tensorflow tutorials
6. TensorFlow Boosted Trees Classifier
7. Lasso (statistics) Wikipedia page)
8. Tikhonov regularizationm Wikipedia page
9. Palczewska A., Palczewski J., Marchese Robinson R., Neagu D. (2014) Interpreting Random Forest Classification Models Using a Feature Contribution Method. In: Bouabana-Tebibel T., Rubin S. (eds) Integration of Reusable Systems. Advances in Intelligent Systems and Computing, vol 263. Springer, Cham
10. S. Aeberhard, D. Coomans and O. de Vel, Comparison of Classifiers in High Dimensional Settings, Tech. Rep. no. 92-02, (1992), Dept. of Computer Science and Dept. of Mathematics and Statistics, James Cook University of North Queensland. (Also submitted to Technometrics).
11. S. Aeberhard, D. Coomans and O. de Vel, “THE CLASSIFICATION PERFORMANCE OF RDA” Tech. Rep. no. 92-01, (1992), Dept. of Computer Science and Dept. of Mathematics and Statistics, James Cook University of North Queensland. (Also submitted to Journal of Chemometrics).

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